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Review

Review. 1. Describing variables. 2. Probability, up to sampling distributions. 3. Statistical inference. Techniques. Describing Variables. 1. Data tables columns = variables independent rows 2. Population vs. sample random variables 3. Describing one discrete variable:

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Review

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  1. Review • 1. Describing variables. • 2. Probability, up to sampling distributions. • 3. Statistical inference. Techniques.

  2. Describing Variables • 1. Data tables • columns = variables • independent rows • 2. Population vs. sample • random variables • 3. Describing one discrete variable: • frequency table = one-way table • pie charts and bar charts

  3. Describing Variables • 4. Describing one continuous variable: • a. measures of center • mean, median, rms, trimmed means • b. measures of spread • standard deviation, variance, IQR • c. frequency tables (with bins) • d. histograms, density curves • unimodal? skewed? normal? • e. percentiles. ogives.

  4. Describing Variables • 5. Describing two discrete variables: • two-way tables • independence • 6. Describing two continuous variables: • scatterplots • associations and correlations • positive-negative? strong-weak? linear? • independent? • 7. Standardizing variables

  5. Probability – Random Variables • 1. Discrete variables • mean • variance • standard deviation • 2. Density curves

  6. Probability – Sampling Distributions • 1. Sampling distribution of a sample mean • 2. Sampling distribution of the z statistic • 3. Sampling distribution of the t statistic • 4. Sampling distribution of a sample proportion • 5. Sampling distribution of the chi-square statistic

  7. Inference - Techniques • 1. Standard errors • mean • proportion • 2. Critical values • 3. Confidence intervals • 4. Hypothesis tests • mean – compare to conjectured value • proportion – compare to conjectured value • difference of means • difference of proportions • one-way tables: do the data match the theory? • two-way tables: are the variables independent?

  8. Regressions • The pictures • The least-squares principle • Diagnostics • s --- standard error (of the residuals) • R2 -- how much variance is “explained” • standard errors of the coefficients

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